A remark on Ext groups for motives with maximal unipotent radicals
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915352433131520 |
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| author | Eskandari, Payman |
| author_facet | Eskandari, Payman |
| contents | Let $\mathbf{T}$ be a neutral tannakian category over a field of characteristic 0. Let $M$ be an object of $\mathbf{T}$ with a filtration $0=F_0M\subsetneq F_1M\subsetneq \cdots\subsetneq F_kM=M$, such that each successive quotient $F_iM/F_{i-1}M$ is semisimple. Assume that the unipotent radical of the tannakian fundamental group of $M$ is as large as it is permitted under the constraints imposed by the filtration $(F_\bullet M)$. In this note, we first describe the $Ext^1$ groups in the tannakian subcategory of $\mathbf{T}$ generated by $M$. We then give two applications for motives, one involving 1-motives and another involving mixed Tate motives, leading to some implications of Grothendieck's period conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_16540 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A remark on Ext groups for motives with maximal unipotent radicals Eskandari, Payman Algebraic Geometry Number Theory Representation Theory 19E15, 14C15, 18M25, 11G99 Let $\mathbf{T}$ be a neutral tannakian category over a field of characteristic 0. Let $M$ be an object of $\mathbf{T}$ with a filtration $0=F_0M\subsetneq F_1M\subsetneq \cdots\subsetneq F_kM=M$, such that each successive quotient $F_iM/F_{i-1}M$ is semisimple. Assume that the unipotent radical of the tannakian fundamental group of $M$ is as large as it is permitted under the constraints imposed by the filtration $(F_\bullet M)$. In this note, we first describe the $Ext^1$ groups in the tannakian subcategory of $\mathbf{T}$ generated by $M$. We then give two applications for motives, one involving 1-motives and another involving mixed Tate motives, leading to some implications of Grothendieck's period conjecture. |
| title | A remark on Ext groups for motives with maximal unipotent radicals |
| topic | Algebraic Geometry Number Theory Representation Theory 19E15, 14C15, 18M25, 11G99 |
| url | https://arxiv.org/abs/2506.16540 |